Two-dimensional phase transition models and λφ4 field theory

Abstract

An overview is given of the results obtained recently in the course of renormalization-group (RG) study of two-dimensional (2D) models. RG functions of the two-dimensional n-vector λφ4 Euclidean field theory are written down up to the five-loop terms and perturbative series are resummed by the Padé - Borel - Leroy techniques. An account for the five-loop term is shown to shift the Wilson fixed point only briefly, leaving it outside the segment formed by the results of the lattice calculations. This is argued to reflect the influence of the non-analytical contribution to the β-function. The evaluation of the critical exponents for n = 1, n = 0 and n = - 1 in the five-loop approximation and comparison of the results with known exact values confirm the conclusion that non-analytical contributions are visible in two dimensions. The estimates obtained on the base of pseudo-ε{lunate} expansions originating from the 5-loop 2D RG series are also discussed.